Problem: Find the greatest common factor of $110, 40,$ and $120$.
Answer: The greatest common factor (GCF) is the largest number that is a factor of $110, 40,$ and $120$. In order to find the GCF, we can factor each number completely as a product of prime numbers: $ \begin{aligned}110 &=2\cdot5\cdot11\\\\\\\\ 40&=2\cdot2\cdot2\cdot5\\\\\\\\ 120&=2\cdot2\cdot2\cdot3\cdot5 \end{aligned}$ Now, let's find the factors that are common to each number: $ \begin{aligned}110 &=2\cdot5\cdot11\\\\\\\\ 40&=2\cdot2\cdot2\cdot5\\\\\\\\ 120&=2\cdot2\cdot2\cdot3\cdot5 \end{aligned}$ Each number shares the factors ${2}$ and ${5},$ so the GCF is $2\cdot5={10}$. The greatest common factor of $110, 40,$ and $120$ is $10$.